Insurance MLR

Expplore and prep the data {r} #stringAsFactors = True will change strings as factors insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE) str(insurance) {r} # summarize the charges variable. Here we can see the min, median, mean, max and 1st quartile and 3rd quartile . Here we are summarzing the expneses the $ between insurance and expense allows us to choose the column expenses summary(insurance$expenses)

```{r} # histogram of insurance charges #Here we can visualize the frequnecy of different values or ranges of values within the dataset. We can see #how spread the datat is spread out across the different values (expenses) within the insurance dataset. #In this datset, expenses are the responsive variable. This is why we choose to select the expenses variable. hist(insurance$expenses)

```{r}
# table of region
#Here we create a table with the regions in the dataset. As mentioned earlier, 
# the $ allows us to choose the column from the dataset. We can use tables in R to create
#frequency tables to summarize the count of occurrences of each category in categorial data
table(insurance$region)

{r} # exploring relationships among features: correlation matrix cor(insurance[c("age", "bmi", "children", "expenses")])

```{r} # visualing relationships among features: scatterplot matrix # If the points tend to rise from left to right (an upward slope), this indicates a positive correlation. As one variable increases, the other variable tends to increase as well. #If the points tend to fall from left to right (a downward slope), this indicates a negative correlation. As one variable increases, the other tends to decrease. #If the points are scattered randomly, with no clear trend, this suggests that there is no correlation between the two variables.

pairs(insurance[c(“age”, “bmi”, “children”, “expenses”)])

```{r}
ins_model <- lm(expenses ~ age + children + bmi + sex + smoker + region,
                data = insurance)
ins_model <- lm(expenses ~ ., data = insurance) # this is equivalent to above

# see the estimated beta coefficients
ins_model

{r} #Step 4 model of performance # see more detail about the estimated beta coefficients #A higher absolute t-value indicates stronger evidence against the null hypothesis. It plays a vital #role in determining statistical significance in hypothesis testing. summary(ins_model) {r} ## Step 5: Improving model performance # add a higher-order "age" term #the relationship between age and cost is not linear, fitting a quadratic term age^2 allows the model to fit the data better and potentially reduce the residual error. insurance$age2 <- insurance$age^2

{r} # add an indicator for BMI >= 30 #we are adding a column called bmi30 #condition: insurance$bmi >= 30 checks if the BMI is greater than or equal to 30. #value_if_true: 1 is assigned if the condition (bmi >= 30) is TRUE (i.e., the person has a BMI of 30 or more). #value_if_false: 0 is assigned if the condition is FALSE (i.e., the person has a BMI less than 30). insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)

{r} # create final model ins_model2 <- lm(expenses ~ age + age2 + children + bmi + sex + bmi30*smoker + region, data = insurance)

{r} summary(ins_model2) {r} # making predictions with the regression model insurance$pred <- predict(ins_model2, insurance) cor(insurance$pred, insurance$expenses)

{r} plot(insurance$pred, insurance$expenses) abline(a = 0, b = 1, col = "blue", lwd = 3, lty = 2)

Use the MLR solution built during class to predict the insurance quote given the following case scenarios:

Case 1: Age=22, Children=1,bmi=27,sex=male,bmi30=0,smoker=yes, region=Southeast. {r} #Case 1: Age=22, Children=3,bmi=24,sex=female,bmi30=0,smoker=no, region=Northwest. predict(ins_model2, data.frame(age = 22, age2 = 30^2, children = 3, bmi = 24, sex = "female", bmi30 = 0, smoker = "no", region = "northeast"))

{r} #Case 2: Age=22, Children=1,bmi=27,sex=male,bmi30=0,smoker=yes, region=Southeast. predict(ins_model2, data.frame(age = 22, age2 = 30^2, children = 1, bmi = 27, sex = "male", bmi30 = 0, smoker = "yes", region = "southeast")) Based on the predictions in Case 1 versus Case 2, we can infer that the cost is likely to be higher for a male living in the South who is a smoker and has a higher BMI, compared to a female living in the Northeast who is a non-smoker with a lower BMI, even though she has more children.